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Maths

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A straight river flows at a speed of 20km/h. A boater starts at the south shore and heads in ths direction of 70degrees from the shore. The boat has a speed of 20km/h in still water. Find the true speed and direction of the boat.

  • Maths -

    Let the river flow in the +x direction.
    Across the river is then +y.

    river velocity = (20,0)
    boat velocity relative to the water
    = (20cos70°,20sin70°) = (6.84,18.79)

    resultant velocity relative to land
    = (26.84,18.79)

    speed: √(26.8^2+18.79^2) = 32.73
    direction:
    tanθ = y/x = 18.79/26.84 = .70
    θ = 35°

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